Then each source robot synthesizes its discrete plan using the algorithm in [1]} and the package [2]}.
It took approximately \(0.03s\) , \(0.05s\)  and \(0.01s\)  for the above three groups to synthesize their discrete plans.
For instance, \(a_0\)  has prefix cost \(57.22\)  and suffix cost \(46.14\) , while \(a_3\)  has prefix cost \(60.60\)  and suffix cost \(45.69\) .
It took \(0.3s\)  by Gurobi [3]} to find the optimal solution of (REF ), which determines the initial paths of all relay robots.
The discrete plans are executed according to Section REF , while the data are transferred and uploaded during the meeting events as described in Section REF .
The coordination for the next meeting event and spontaneous meetings follow Sections REF  and REF .
We simulate the system for \(100s\) . A snapshot of the simulation at \(40s\)  is shown in Figure REF , where we show the number of data units stored at each robot's buffer and the action taken by each robot.
The evolution of the stored data units at each robot's buffer is shown in Figure REF .
The maximum number of connected robots remains below 5 during most of the simulation, as shown in Figure REF . Thus the communication network among the robots is almost never connected.
Furthermore, we also monitor the times that relay robots \(l_0,l_1,l_2\)  swap meeting events as described in Section REF . Figure REF  shows the reduction in total waiting time after two relay robots swapping their meeting events.
In total, 137 units of data are uploaded, as shown in Table REF  and Figure REF .
The complete simulation videos can be found in [4]}.
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